ATHENS/ROME (Reuters) - With efforts to patch together a Greek government looking doomed, EU policymakers warned the country it could not remain in the euro zone if it ripped up its bailout programme, and financial markets ratcheted up the pressure on the bloc.

Eight days after inconclusive elections, Greece's political parties have failed to form a coalition and opinion polls show that anti-bailout parties would perform most strongly in a fresh vote which is likely next month.

Last ditch talks led by President Karolos Papoulias on Monday looked unlikely to make headway after the leader of the radical leftist SYRIZA party said he would not attend and another left-wing leader refused to take part in any coalition without him.

Finland's European affairs minister said Greece could not remain in the euro zone if it tears up its bailout deal with the EU and IMF - the central demand of SYRIZA leader Alexis Tsipras, 37. "I think that is an impossible equation and I think in that sense it is an irresponsible statement," Alexander Stubb said.

With Greece set to run out of money as early as next month and no new government in place to negotiate the next aid instalment, investors have begun betting that a chaotic Greek default and euro exit will happen sooner rather than later.

Talk of any member exiting the euro zone used to be a taboo for policymakers. Not any more.

Over the weekend, European Central Bank policymakers Luc Coene and Patrick Honohan both openly voiced the possibility of Greece leaving the currency bloc and concluded that it would not be fatal for the euro zone.

But there are powerful incentives for keeping Greece afloat, not least that the ECB and euro zone governments are major holders of Greek government debt.

A hard default could leave them with heavy losses and if the ECB needed recapitalising as a result, that bill would also fall on its members' governments, with Germany first in line.

"We wish Greece will remain in the euro ... but it must respect its commitments," European Commission spokeswoman Pia Ahrenkilde Hansen told a regular news briefing.

Euro zone finance ministers meeting later are expected to discuss the possibility of granting heavily indebted Spain more time to reach its budget targets, as well as Greece's situation.

If Madrid could be cut more slack, Greek politicians will ask why not Athens too?

CONTAGION

The biggest fear for the euro zone is that chaos in Greece could drag the much larger economies of Spain and Italy down and threaten the entire currency area's existence, a risk markets are beginning to price in.

"If Greece moves towards exiting the euro ... the EU would then need to enlarge its bailout funds and prepare other emergency measures," said Charles Grant, director of the Centre for European Reform think-tank in London.

The cost of insuring Spanish government debt against default hit an all-time high on Monday and the premium investors demand to hold Spain's debt rather than Germany's reached its highest point in the currency bloc's history.

That stress did not, however, weigh too heavily on debt sales by Italy and Spain.

Italy's borrowing costs rose at an auction but it paid less to borrow over three years than trading prices had suggested beforehand and it sold the maximum planned amount of 5.25 billion euros.

Spain, beset by concerns about its banking system despite moves last week to shore it up, raised 2.9 billion euros in 12- and 18-month Treasury bills, with yields on the shorter paper up by around a seventh from the last such sale in April.

"There's a real risk for the market that at some point Greece will have to leave the euro if they don't find political cohesion ... This will add to the contagion in the market and the countries that will suffer more are Spain and Italy," ING strategist Alessandro Giansanti said.

Greek polls offer a glimmer of hope, showing a public overwhelmingly against more austerity but up to 80 percent in favour of remaining in the euro zone.

If the mainstream parties, New Democracy and PASOK, could turn a fresh election into a referendum on euro membership and convince the public that SYRIZA would provoke Greece's ejection, they could fare better than on May 6, when their combined vote was more than halved.

"This time, whether we like or not, they will be more like a referendum. We will have set ourselves the question whether we prefer the euro or the drachma," centre-left daily Ethnos wrote in an editorial.

PASOK leader Evangelos Venizelos, who as finance minister negotiated Greece's second, 130 billion euros bailout, has pressed for its lenders to give it three years instead of two to make the necessary spending cuts to bring debt down.

SEARCH FOR GROWTH

As always, decision-making will rest first and foremost with Germany and Chancellor Angela Merkel, who has insisted that tough debt-cutting programmes are the primary route back to health for the euro zone.

Merkel conservatives suffered a crushing defeat on Sunday in an election in Germany's most populous state, a result which could embolden the left opposition to step up attacks on her European austerity policies.

New French President Francois Hollande will visit Merkel in Berlin on Tuesday after he is inaugurated to press for a European growth strategy. Germany has not opposed the idea but insists it cannot be funded by extra government spending that would drive debt back up.

"They should tell the Greeks that if they wish to stay in the euro they cannot avoid austerity and structural reform," Grant said. "But to raise the Greeks' morale the EU will have to relax Greece's deficit reduction targets, write off much more Greek debt and think more imaginatively about how to encourage external investment in Greece. Merkel will find such policies harder to embrace than Hollande."

Investors are already looking to the ECB to return to the fray. It created more than 1 trillion euros of three-year money in December and February and signalled afterwards that it had done all it could.

"We expect the ECB to ease policy, maybe through unconventional policies in coming months to support the situation in the (euro zone's) periphery," said Raghav Subbarao, currency strategist at Barclays.

Just as the ECB revived its bond-buying programme last year to prop up Italy when it was drawn into the crisis, so Italy is likely to mark the threshold for any fresh intervention.

Europe's beefed-up bailout fund may have the resources to protect Spain if needed but Italy is bigger and most analysts believe it would need ECB help if sucked into the storm again.

(Reporting by Renee Maltezou and George Georgiopoulos in Athens, Valentina Za in Milan, Paul Day in Madrid, Emelia Sithole-Matarise in London; writing by Mike Peacock; editing by David Stamp)

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